Kupiec unconditional-coverage LR test for VaR exceedances

Under the null the exceedance indicator is i.i.d. Bernoulli(alpha), so LR_uc = -2 log[ (1-p)^(T-N) p^N / ((1-N/T)^(T-N) (N/T)^N ) ] is asymptotically chi-square on 1 df. This tests coverage ONLY: a model that puts every breach in one cluster passes it. Pair it with morie_christoffersen_cc.

Usage

morie_kupiec_var_test(hits, alpha = 0.05)

Arguments

hits

0/1 exceedance indicator.

alpha

the VaR tail probability the model claims.

Value

list: statistic, pvalue, n_obs, n_exceedances, expected_exceedances, rate, df, alpha, method.

References

Kupiec, P. H. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives 3(2), 73-84. Cross-checked against rugarch's .LR.uc.

Examples

morie_kupiec_var_test(c(rep(0, 90), rep(1, 10)), 0.05)$statistic
#> [1] 4.130844